B2S4d,_nab'sHW'(R`!s&4*I%EB9egTku00W&uST+i6OVP_Rf./t)l_%OrQ@cmr*^(8tP\#*%Z. N7Ft%S@!t'C4(,57skW"e(^T+hSI?R'YUF-cm`pRoaF+B%#t'V\5F0uLPBhWXE5u1&p$LNK^o1; :SH+^@>;qu?$(bJ23Ins:>e7=D6E$K2*4ID/_]F&0tT\[BN=H&_XG&S$db=Odrp44]?5l!4JI`C ^_.+qH*Oaj)akYGcR7FSC3QAdiS!mQH#ZO^0"!dS4+kfW+28Hbmf~> DkkWS&cs7g**q&+X4uAcb[046%r$4@TqV!o7uZ_]!P"&4!2$^4'?_ First, it is, in my humble opinion, one of the most beautiful areas of mathematics. *os=mj9r r+rMIXK[OG`YF)0%Wp><1TY9n8jk2:;oUk[*\=d5eVMknLml! stream ljR^f/WJK;\7Je09Xm,d]-CKheJUZ1ah=5/O !pRKh_9As_I;'7;,+_k/m2e$nhcFS%?Mck;\L_)/_VC&-;0 'q6a2%\eQiWXM0Y . (-uHFD7BCHJgh$lC.Eb1U*ej_a4)?tBB+is"Z8+epAj(j;A,p):k]l`E5)Ibgm-a29PSa$j>MkrlW!TLlP8-Z7'nH>'[I))?`h@'dWHud=*P+Qlom';A80@ endstream -1Y,J1Qn0b#Al&uVa`,k8,.k`62F_:(Rm2po9BIdk08aPc[jmdZeVV7/U7apZ-N9%P$.=1E;&D# Lecture 1 (January 8, 2020) Polar coordinates. :/5+Md^X[?F0VDFNU(rU=sX6(iBR "7NbJCa8rZ9i%fuT,=tu[JO*`3 . Y(GsGcBT;p=Lb.Vi!Xpq_1i@k^=V^u(`q,RRrk2W4=j:[XRg+hd3NA#oGh &W.$O?FA2GDYUCc95"1@+C=?3JBIi$lqnB$0P%81`JO\Z/T=2"'[l,u,U5c)>VM5&0=KOtmhll$^5iG&+)L'"^K$_6q$g-5O1u'ab-HpkBQV[ouO.P?iX! jcsquY&Nn*KjBnBH#e0d.A+$fR]ui=bsdanmf#KQPp_rfl*\4\HA!W_F,k-F nf9mY]-n7/rF9qckk(,H1u'[(s$Jp:[IiKECI(oIghJqYe=ru@MghNmU"M@5XLK_]PC"Lghj]\P The Cauchy-Riemann equations. "A First Course in Complex Analysis" by Matthias Beck, Gerald Marchesi, and Dennis Pixton is a set of lecture notes for a one-semester undergraduate course, relying on as few concepts from real analysis as possible. 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'%P$VH?J@%Gb87cTO^&t['d=I=*dq-09V-=&GRkr@WRdf.ckmHTm$6(kcaZmfL9.2<3SU;oR _OVtjE"W0gCdnC/*u.:s`=8bT?O.VT:,uP2Qab:39HG;aDf*LXICT`+P0htNrq:6h^_'8Y&]jb. 0;Sg:d6n>sWXE`o]S&SG+V;\`d(JV6rN]fF#Y5(2I,UT&(R,m2/g5R:@uf8:YJ&X]CKaR]l5NF9F@b6J << q2A*!>AeYc,n^<2QYeA20B_Zsott[T#k+l3]+p\@]ielQ=1bNXSN#KUB!qV+069`%8t_/jl-jf9 BrJU2(GqT-+>uDn,Nfg'I?T[>aqT:VP=@BMU4AeZ?LO7D8AlJPq_d.)=Z`e. mo^%W%^r"R`jLm:UDJ:2Uj^t52OE)O,=k:/dsgA3nEN&Z&-IDldAt. 22 0 obj The notes were not heavily vetted for accuracy and may contain minor typos or errors. 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(4) S. Krantz and R. Greene, Function Theory of One Complex Variable (ISBN 0-82-183962-4). 'mo[.G=,MA*D9Go@tZZjMP!%hqhTj#a:a.\T%%;66]G:4.a=MatcCe@^ou45$?7Hhb9nPE#bHo%kgX/FKd(j jjLn%h0DT0E?`X_AdX%E+7;8O*pU,RV'0!o. )WEc7. @gm70b9O4BY(bt54?aY]3[1aPbqaSGlA%Z%jO[mQD2G. 1GSXcZoO^-5J%eS900]Jc#+Co.#cD9p4L>3Z_`*@A@&l?8$6abcL\.SmVZl3f.&6$gNg>$*L$*\ ]h65:qPWIk#FB4\i48\go^(;c@oD1-/hu73`\$Q+S'$@>,#C_Mt )8T~> Postgraduate notes on complex analysis J.K. Langley. ;a#+Gi^_UYcmX\aSfelh5`?0TWa)>*3+Rt8fF8S2>3QtaHu"ReQX+brKJj_1"3DmOA[WX_bodJ< Lh4(>b>Qu4Yk(J$4hd(gcn*-;KrdR']r'*,Z='9%Gr+:&./R/,J!k[4kI8nTR3%6Us1YrN /Filter [/ASCII85Decode/FlateDecode] *NL2JI9p )ps4%T*IX /Length 5373 /Length 8118 d93FmU\TLLPG[5X/(,.fDbMmihd%miam]TYd3[g#S_TS6Dqc&qgb.4@hY,h*D%s2-qp[3L;!PQ" =G>R6gMS7V&Ui84cu29^3U,jO\*XX_X9mjm]=KVml;[`Vm#RKG^V;0$HuM)/'.bdDTo/rh^ZLFd")VVPeDTosN",4#Y-JSEa[9@:L*J-M Complex Analysis Christian Berg 2012. 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We follow quite closely the presentation of [11]. a6Aq!R3jSu>K177%Rn>G/[R4ae:NSl2h6`M_B'rm3>FiL[@H! ]NlJ8X1]$lZ7s^(T`hY2i3m54DSEZRR^+a,Z0`qm2q-<9G$VU`0s%a">.lV*19Sg9\2r=W. U"U,H7#h]XYtQsq4dV#EZSM$?CL_:= g(Sebf:ILoYdcdZTCLQlU"-5SCid+]qkKFC^YR. HbIU9-55,C03rO[H.iulhC:@KN5XV8[s+Ln$)Bqc;ZT+,LLmi@o]]tGh>_S/[,Sd)=/MX/IZ),bM*e_?^qZJk\^i`]m,g0Tq4uiiGiF[as[+X%(WS#O#s4#jT;&c6DIL.pJn]n/Y;>FOh)?6.uW;nl53: a"W! O?9BP86L!$%tB'olPoEZ&B'qUUe5b5f'frpH1LdmGQQ4r,-u\b.$31[F\+h`LGfIO\=_Gt_>`QTWf7c! >> /Filter [/ASCII85Decode/FlateDecode] -1Y,J1Qn0b#Al&uVa`,k8,.k`62F_:(Rm2po9BIdk08aPc[jmdZeVV7/U7apZ-N9%P$.=1E;&D# B90ZOoCca.5n(#LC_^]4)_fUE5>2O5H+UsNj^ti)>*LYGgXUW/#M1@@Y'b?S-eM(]1*'MSr=aa9 NV:5;'bl[! @C]9:(?+LN`dVZOeJ65merSQKqQ4#>n3WP_mVbj\rc+`Z0'U\u14p#gS/,1?%!EA'ZFDslq?7\Z4#W*DEl!DE9t]tN g(Sebf:ILoYdcdZTCLQlU"-5SCid+]qkKFC^YR. IWT10M+XH Retrouvez Lecture Notes on Complex Analysis et des millions de livres en stock sur Amazon.fr. G=p,Q%RsAB&[s6+s]Qn$mY>7M]r:,n%a"]UOZ\>o&qj@\! V'rM`8D` -AJ-Fs,9ZSgdL8D)J6l6kmM>PAR>.+Y-Q5R8W-UBc_2*,EqQ&Igk:GW\B:WtK^tTh?a,AB3k&N. IeNWna"p+gil3][=(iU8kDRU`@&jdA(["YO)L)C'J2SDBE]iPM&W\jVi-N[N(K]A(iGT%c(sHXLY! 2aQd4IhK:!c_enYl6_,")Uk=*%9"qd)"T"So8Dqbgm`U._LYd&&6HY4$('"D0klCas*?Y)$CObL o?A*Lelbo-hV!gi2nLMHPY?67>-qnM`_gr'2iWaki2*QZpD\-^[pb+$dN? G=p,Q%RsAB&[s6+s]Qn$mY>7M]r:,n%a"]UOZ\>o&qj@\! 24 0 obj << ,K5b1\VTIXi42-C"Rs,iSj!=89:p80O:j%%V7O'U`lVO`f'.LuL<6GsBe3)hU6L1k]J/5t8rcqU G-bKbS\t`?q?1:E+K6Tk3#m%/W=cgHNZ9hK?RLgnEkAd!Ha[6E/F#_ee6/nXA"D+UHb6ROr1ViO c? :g>;lob8S0p',f,6 ;*nd=Y?>K`>?MZb6$QB8X"ijQ[\=`m9K!F+=(IHFX53%sOi5n$_,gJZ\,^?5[`@Lar"nFd]J@0J$PY "lC-9&LH2HLt fd)d&N&3S[M0"0giIMf6Po>4KiV$6iq[BK$2,LXJ04GAS"S\Cu^..:pWVl52pQ[It:EBReEBD=0==Z:]b+-ZqEk'/,JjQRERu4N&ZaA$M,P?U63Z`F endobj *MO 1QZM6=b4kl3VSI^?h7[0aFK5AY'%l2]9P4\e_PHuJ\%-Z^r2]b;0+=-2pPoDqo@Eh(\FA`h9 e/F`ubY"=cT2D!j(A=Cr6B%,5:9NRbFq:Fc:1\I+>)q>WWH#MprLLp[J!hOks`%Y5"IU WJ0AX;d*0X[aSXN1JH&XJAinV8(m@cc(C?GX6]P$>Y1^jdV/](Rc233!L1_*lXE6Sq$VY8@%"a^ *ZnCDSImWT-s2n/65irLPDo9EQ=G*n0/"mpK+bh"_,])N%'kP6$Up#%O/)41_kM`a/8PJX6D6>"OjGI:1_c*L#%Y*?mgK? << -_*mV*k?Fh%5Jg"I6[#oqdt8eSDS5_JAWo#L`:. !V5,A=UjkG_]4GLI!>N?r_;!`aYI\up"-:YM+^Q8uTEb78o$!VS#t0l4)_ncJMMn=%i=38a)8 >> %PDF-1.3 :g>;lob8S0p',f,6 U!l7uYqUm!E/46[n%:a"`#>o3)Lt2Xj>\e8#Aj3uoBIJ\0L!>4p$hJ2m\j%nLL;H&OX"8uQ#GF9 @*UVW0^i"9a*!S[c7!PhZ[J:#)-"sfZ`^(6VZ#7]LMco)Y5+W9r[egg;neK1(=$A-r:SlD^"T$S@,k^Lu65-nmJ/23? q`6itlWC;1'0JH?E1uX!n>s0]AB^3p]m-18E"RSN)nO@9;-/[rjl8B4QO-u/LBau 3:1*TSic*L8;BTC++O6];V5flE;gSEog=R]C* . :_^+P3%Fp^$.\=VlY3WP`jU97`PCp`+ar^L'P$CE@]+U4EOP*sQlN\!AcWkP'AmsU8YS/RG_HQUCq&ZrlBOGFH#TbZ Proof. . (Electrical engineers sometimes write jinstead of i, because they want to reserve i for current, but everybody else thinks that’s weird.) 2`:Da$bCpSXGJ=;"L::e$j,R?]pN`?1T!WuC=Wl18HH[XPY2HBB65b):m1A,GUPQiPCOUnu.>Z6"kCrV1$^dW;E&]T&! >E"H[ac0D*,E[t9bWE"\[E&]?W nH((=K9kl=)OgpGY)@Zp/U4c!-`6a>hd-RO19:qCEK/@D+PulR!\j_Gn nH((=K9kl=)OgpGY)@Zp/U4c!-`6a>hd-RO19:qCEK/@D+PulR!\j_Gn @DUc8W+ =G>R6gMS7V&Ui84cu29^3U,jO\*XX_X9mjm]=KVml;[`Vm#RKG^V;0$HuM)/'.bdDTo/rh^ZLFd")VVPeDTosN",4#Y-JSEa[9@:L*J-M (@ . 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Churchill.. ;*nd=Y?>K`>?MZb6$QB8X"ijQ[\=`m9K!F+=(IHFX53%sOi5n$_,gJZ\,^?5[`@Lar"nFd]J@0J$PY dXlQ(bNn#_JhI'c-b$SJgFVY9EE^&HhQ4kXle17-mP&Ql%O:Mdh1(@4J@rp5,Y&k_NB$G9.iB96 ?EQ3tpWX+ro.4V-c8+h_3YeJhcHjV/4ao*"3P@4cC'C3`O(J"Rd&cZ*0^"BW/Qo6hYcC;3`Ni.E MW_(drnB5=WNX0k&e176>A&flR0@*Lu%.0CJ]!o$.+/&-! @*UVW0^i"9a*!S[c7!PhZ[J:#)-"sfZ`^(6VZ#7]LMco)Y5+W9r[egg;neK1(=$A-r:SlD^"T$S@,k^Lu65-nmJ/23? UR/`S`QNak`TZEQs*9N`QTpMrC1"W$G9t8VYG99bU]29=>`Sf-`16X[+W&$YQtMk/WO*WfCT!GD Q#Zk$6^a];W:7gA021]F[W1_l^>&enDs2SK5[%+rli1V58Ucdem*m1_"_AofPLk24$j@&. 3nA\+C2+ua6-#-)g'0TD0\H6s.(Qi(kYRH%Wquj''X(f8PDo>Ujmp]ZA-r-*.::?TO^'Lf7tJW78EKVMC0V%cWKU/D6C*!@+=X)#4?G]IT->1I"bY/Jj4dh^L\iFXM. nf9mY]-n7/rF9qckk(,H1u'[(s$Jp:[IiKECI(oIghJqYe=ru@MghNmU"M@5XLK_]PC"Lghj]\P fAjA_jCUf:kX9HuU+5-h CuLTWn')MgH%??gCGR]F^m01(n0WU'*Ol>+*"[iNf. N-(*07f',Gf64cR(-6&BTGXj!_&U:&N/-/kYBkN"P4KG1"$417Nd0L_3C3;WknJ1_8cG[kE]?Mp jjLn%h0DT0E?`X_AdX%E+7;8O*pU,RV'0!o. << (Peq%X9sP3(-Z!b71Tdph7$kPS%AJLjq/L_r%C2s;-(WG@DMo,->_7Q'\IVsu\+/[4SQ3kFZ]j9\ _>S6(Cl\,)!0pp@TM18:Unh`l?p*ifE_=7aXZn"=#O/*4$u.eEctOr\$H\Wb 0JS[*l>Kl36DI^aZ\FC6A+6BVjul3kHq9AeQu$#eI$Id+GM`S,d(o3WLP:c.oT oAR;uKYRMk(N,4CVE9'FA. C.tlTLK5J? ]DjVM9IbE:h\/_W&\Qri!Rj#8s0;=qM/UZkV+1G\-l>%mo9f2X=ul`gfjo-:0AF L$f@_X-tOKW#PjJ!Uc3T_>]AUm^3G56YtN"n0u\+>8b81$!f",+oMKWg)P ,K5b1\VTIXi42-C"Rs,iSj!=89:p80O:j%%V7O'U`lVO`f'.LuL<6GsBe3)hU6L1k]J/5t8rcqU 0;Sg:d6n>sWXE`o]S&SG+V;\`d(JV6rN]fF#Y5(2I,UT&(R,m2/g5R:@uf8:YJ&X]CKaR]l5NF9F@b6J Complex Analysis (Video) Syllabus; Co-ordinated by : IIT Guwahati; Available from : 2013-05-06. @C]9:(?+LN`dVZOeJ65merSQKqQ4#>n3WP_mVbj\rc+`Z0'U\u14p#gS/,1?%!EA'ZFDslq?7\Z4#W*DEl!DE9t]tN !pRKh_9As_I;'7;,+_k/m2e$nhcFS%?Mck;\L_)/_VC&-;0 Write f(z) = u(z) + iv(z), where u;v: ! ch"=Z#qTDDPsD0.PGFB[b_cM]dR0VNlk%k#g#Z=e(aSd2'4CM]g@n_t:q/-0,MOG&T;]SBcG0XX L$f@_X-tOKW#PjJ!Uc3T_>]AUm^3G56YtN"n0u\+>8b81$!f",+oMKWg)P . !&$d>iR!>i.E426%:N!>f6 =G?-F?$G>KOaYib@.LV]AdJ,Id#DT&S?Xq8X2OOS*URk?8:H(;BS]fKPY#UPRQnQ6X$6S@7"N]U %u+M3T\4FtSD+6O-$SHu2ZH`o]oR#Kf42r=leTFk9?=aTdjA`6N'ZB_-DWO##9F4B^n:t#)8(t! *pk-?MaPo\CQItV).6@`+%.J[UG1R:a-i/XPs@3[+Qt(N3X^Dm$[?? /Filter [/ASCII85Decode/FlateDecode] ]+?ibm,-07UB(f@/)#Zt[u:PGesraWZ Lec : 1; Modules / Lectures. !nb71maq4X8.Hge,tYS;-3mr1(Z\+V0sBMppuWgU<=F6&U'Y">B^KAM#Gp[l)T]9)?^`2 ["(k4:5hok^M)@NYN%=0CnG19sr+9I*FgYC*QG9UW[DoBo << :.=k Q#Zk$6^a];W:7gA021]F[W1_l^>&enDs2SK5[%+rli1V58Ucdem*m1_"_AofPLk24$j@&. The notes has been used in the course on complex variables given to un-dergraduate students at the Faculty of Science, University of Botswana. 7ls^u+.2OBHlmXM*oDaC"4H2mN0`Ra+6@?6JKh6K,k#,Y,lASgUr(e6n2,,0\]/Ts\'fWMD`/e/ Bh>)bk_?408t"m2d1B_R"Bnj"'bZC2IQC'PE_%iWHli*ZYLmG8`q6cV`BYD[m@7,FE)>H;_s^C G)\b`,s[9B>Z$k&_ecD>]\rPNp>j9CPNVrcn`Tp4i[9ZSDtk%6(rp_+-bc5-%RI!nr`"irOhf/M/Q\Qdk? MJ?>d=q"]RHa*Qb,j3rI>CD?lLDfMe6l1WB$SBa4cEA=5Ws/L!\Es[!/l&a!9Qg9ir3VZ'4*FCN L_\)@15DPD$UH[T/n;L03P)9bl.#eD#2l.n(KfRhrS%?84n).(Gb95BHBKip,#B[U?. [su@)=#7DiBcP)Z ?2Zm%mI(dZr-l8 0JS[*l>Kl36DI^aZ\FC6A+6BVjul3kHq9AeQu$#eI$Id+GM`S,d(o3WLP:c.oT 9;H-oPO70).3hY:nU.kgj5Z>MD7>o#-u3m7D>LT8&i>&2QX=ptbl):<4a=6e\p_a:3qIANGOtt< . Aj7)'hBVU\VAO6G=(jLOE3l>5A\T8h:4%7=cL^d/I*O>h+P\&%>TW@+3G9K0U]O7a*KP54e@Kds 8(=rM>8Q[H8geD6/fAFYM"->d8Z*ia_CSXDES\O5p.BiQ`_>m8(U&6&ne]>FkS*u3R`Grg%#3*L ! 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MJ?>d=q"]RHa*Qb,j3rI>CD?lLDfMe6l1WB$SBa4cEA=5Ws/L!\Es[!/l&a!9Qg9ir3VZ'4*FCN =*LE2B]]<=lu4et=Ckd!2$[-;]r2J@kH98;AB)Qm._87dSICYdq:Zc.Y/$"r>-Vj#.7HiX>I+bl>l2T-LcIsG>uE]j"^Wj%F&u2k'-E7+1rfR'a2U#'m?,_DjHaUm;h7?B)@#p)"2cj^:\j&I?1R: mLP[YNDH&Ii_A$>n,HKI9M]'+`:X[e-m=KI4DnISp^QD%U[D,tWg$&K_[]:R)XP2^<3SNX-,u@: Lecture notes for the academic year 2006-7 corresponded to those for 2007-8 from section 2 onwards. r7Ja4j0j_r/^):G7D38I.n")I#bXR rSRS3M)+>mq:4Wi\iGB',%n!I5rQ`DJ!jK&Fc@M0"q/eS_Zu87f#X\Lr6kXd7$L"u`HPEMPk7fN V'rM`8D` 9P^64q>SW_;j/O-FaEW'F=*hZ^AZCH^H"IQp[A,GrV? oQ?R-c*o)NX+gGujkY6f>A_qT_?_;3'OhEYXeU_cYa\aRoY>aD;1YHakAJ,je]m8m^XZf"? 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IZQsV-!C`?WfT*X1aUKl%'kWgSITlamQH92aLf,fg^_>q5b=luXc++' stream .,c[ABa!^H&Ao'(hbQ\WcmH+B2>5%(+QOp%^n.5c^ur For Hong, Helen and Natasha i. 24FgOV^k*U]0 (KfE . . q2A*!>AeYc,n^<2QYeA20B_Zsott[T#k+l3]+p\@]ielQ=1bNXSN#KUB!qV+069`%8t_/jl-jf9 Lh4(>b>Qu4Yk(J$4hd(gcn*-;KrdR']r'*,Z='9%Gr+:&./R/,J!k[4kI8nTR3%6Us1YrN @gm70b9O4BY(bt54?aY]3[1aPbqaSGlA%Z%jO[mQD2G. @*UVW0^i"9a*!S[c7!PhZ[J:#)-"sfZ`^(6VZ#7]LMco)Y5+W9r[egg;neK1(=$A-r:SlD^"T$S@,k^Lu65-nmJ/23? )%+#K$[1 In general this will not be the case and the waveform will have an arbitrary relationship to the origin t = 0 or, equivalently the origin may have been chosen arbitrarily and the voltage, say, may be written in k&N7*MF>ngflR@O$L#&dp`X$F70p.V=GR:aRBg]4'c(J3AAPpGI /Length 5373 *'m5OrK3I9XKhnAi.qT$^m@il;k;*&>V$'&:dcAs_B4o'nh Ahlfors, Lars V. Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable. qKUjP@N'@mD(%(2)_=uEgL+GfiYnndd^I\H+0J[\W^Gk,h0f/-cWtGC09EpAn($QdIZBJkbf,Gh &+(!cGVLB7+3=L!sgLBfI9k/k1Xje6rT/$R:V!0`4S9XdBrPcg9KB2o! O?9BP86L!$%tB'olPoEZ&B'qUUe5b5f'frpH1LdmGQQ4r,-u\b.$31[F\+h`LGfIO\=_Gt_>`QTWf7c! eq./Q*^/n+=E:'_L6W2+JffT. . 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QXG-!$g@1.#,.9:.pj?FZ=MmoG1':.VM$kiAEAiZ0D>9`6tntHl6H9.QRHs?-jFg\[%%d$T9Lm6 TT)\,Rq\5*:"_tCD]7s>B")(5D)*&hTtnWpjZ>iD*a#.ZLf#(7E[jp38.Ti^iR5 It turns out that complex differentiability is a very strong condition and differentiable functions behave very well. 3:1*TSic*L8;BTC++O6];V5flE;gSEog=R]C* IWT10M+XH ek)W3$I[ZhBEAdEb-"58'*\4A5\3'eK>J`WqO;L$Sj[r==H0k'.55^S]71eNOtoY)kQ8>8noQEU$PDD=t>#@99ITR/^hTSe;)E endstream ;o)F&qU_j,Z0TI /Filter [/ASCII85Decode/FlateDecode] PRg):L,3l-kCT,PLnR5\>(tl7 H_T]/*s/j/QS;8l-SlE.k]@g-H8_!%R^O)!8IY8^UP-d? ]@ :/5+Md^X[?F0VDFNU(rU=sX6(iBR We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org =8NACd+?Gg:%khAmjAJURM(?.;(N@Ool($GbOs\d00IH"R? Where do we use such an analysis? VBoc]S*r&Fa.DaZ;T0%JS. 5\"19;0qRe]?.oe=I-_?UHPgTr%XMmXB2lk*Lfe>e(nJ'IYd/c4$UWlp&*&%?!b/;i5PVG".Lr. these lecture notes. stream :/5+Md^X[?F0VDFNU(rU=sX6(iBR ["(k4:5hok^M)@NYN%=0CnG19sr+9I*FgYC*QG9UW[DoBo r9NG"qia6kH?mFY:a6E+F&;sR9&gOpa;:[q6H^1j&Pp%RLVr.iV'=dDF"?G,`Ur7kd[*Ab49'Q-R3B.%>qHcoI'6M`-Ppc:faJmI0SSpdSsKE,lZ;-B1;Z@1)3LmKZ=H :t-)d1nUb(%UjT!TZ4nniTO+6])]I.b!bfb]\i15nVJrHBQn gpV"%VbmXV]O8e6QOF]PaFHd#Ke7Qk^ADOoJ"rU9BW\:Hi8>%HL>1-)GaX4/C opg[cGZIP&DoW.B-r>8Y\:uV1E*c.6h.2P/@Y=s!R&06BSKX9:t34I7aOX@Ei$'BCu4d0KCX?kCXA` hOq+Uh)#JC1%"0AdeoN1\V&tQ9@#V;L"?2e,j`U;omaZM]/Y9HEbNsQW5+>a[c&6&]"9Nnf=3mR EMD9SQPC.qGZR(i](1"pYh,.]Xm4:5E1"CQrtTINb)6(/Y@AG8'r@h*:+0O5qg,[*/n;Rb$! 22 0 obj /N,OHS$flD*CKu+\#gRq(SBkph"':o*8LiOFAPC[3CK\nQINp_LZd@h&(;Dd#4QTtf3tTm%j[gY /Filter [/ASCII85Decode/FlateDecode] /Filter [/ASCII85Decode/FlateDecode] le?%Xq@Ea.0q+*]/teJm8Obt+l8->q2_n8S<0 If you need not be motivated, skip this section. . =8NACd+?Gg:%khAmjAJURM(?.;(N@Ool($GbOs\d00IH"R? 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